With 11 league matches to play, the seventh-placed Reds finds themselves nine points adrift of Tottenham, who occupy the final Champions League spot.

A more realistic target is the Europa League but only fifth place would guarantee qualification, while sixth would be good enough if both FA Cup finalists qualify for Europe by their league position.

“There might not be a trophy at stake but there’s still a lot to play for,” Kennedy said.

“Being in Europe is vital for a club of Liverpool’s stature. It was a special night on Thursday with the crowd playing their part and we came so close to pulling it off.

“Some of our players won’t have played in an atmosphere like that before. They won’t have experienced anything like that but having had a taste of it they should want more.

“Hopefully that will inspire them for the rest of the season. Being out of all the cups means we have to work doubly hard to make sure we get everything we can from the remaining league games.

“We need to get more consistency with our results and finish as high as we possibly can. Too often this season little lapses in concentration have cost us and we’ve found ourselves chasing games we were in control of.

“We need to begin every game with the kind of mentality and attitude we showed against Zenit. That has to start against Wigan next Saturday.”

Kennedy, who made 359 appearances for the Reds between 1978 and 1985, was buoyed by the character Liverpool showed on Thursday night after a nightmare start.

Jamie Carragher’s error allowed Hulk to fire Zenit ahead but the former Reds full-back insists the vice-captain could hold his head high.

“I thought Jamie had a fantastic game and I told his dad that afterwards,” Kennedy said.

“He wasn’t fazed by what happened and led by example. Okay, he made one mistake which got punished but that’s not the reason we got knocked out.

“The fact is in the first leg we created three or four really good chances over there and should have come back with at least one away goal.

“Even in the second leg after Hulk scored we had enough chances to get the four goals we needed. It didn’t quite work out the way we wanted but it was a great performance. Everyone fought so hard to get back in the game.

“At 3-1 with half an hour to go it was on but it just wasn’t to be. The players couldn’t have given it any more. We just needed a bit of luck.”

Kennedy admits he was in awe of the brilliance of Luis Suarez. The Uruguayan striker took his tally for the season to 25 goals with two stunning free-kicks.

“Suarez is such a special player,” Kennedy said.

“Even Phil Neal and I were on our feet when his second goal went in! How far he bent the ball around the wall was incredible.

“For the first one, people say he hit it straight at the wall but he saw that gap and went for it.

“Suarez has had a phenomenal season. He’s only one behind Robin van Persie in the race for the Golden Boot and I’m sure he has his sights set on getting that.

“Defenders are so frightened of him. He turns them so easily and they are wary of putting their foot in. He’s such a talent and his work rate is excellent.

“Every time he gets the ball he looks like he’s going to make something happen.

“Suarez sees things that no-one else sees. I remember the League Cup tie at Stoke last season when he curled one in from way out on the flank. He’s not afraid to try things – even when the odds are stacked against him.”

Suarez’s eye-catching form is bound to attract interest from clubs across Europe this summer.

However, Kennedy insists Liverpool simply cannot afford to sell him at any price.

The 58-year-old believes a strong finish to this campaign would help convince Suarez that the future is bright at Anfield.

Kennedy said: “I’m not sure there’s a club around who could afford to buy Suarez. How much is he worth? He’s priceless.

“His value to the club is massive. He’s a one-off.

“He’s said he’s happy at the club and how much he loves playing for Liverpool.

“The Premier League suits him and he fits perfectly into Liverpool’s style of play.

“Of course he’s ambitious and wants to win trophies but hopefully he will see he can do that at Anfield.

“From the club’s point of view, you can’t afford to allow your best players to leave. We’re building for the future and we need to retain our top talent.

“It’s the same with Glen Johnson, who has been absolutely outstanding.

“Brendan is still building the team the way he wants it and I’m sure he will be looking to strengthen in a number of areas this summer. We need to build around our best players.

“If we finish this season with a great run it will give Suarez extra belief that the club is going in the right direction and can really push on next season.”